y=mx+b is the slope intercept form of a line equation. m is the slope. The derivative of a function at a point is the slope of the tangent line to the function at that point.
In other words, if you know the equation of the tangent line to a function is y=mx+b, then the value of the derivative of the function at that point x is f'(x) = m, the slope of the tangent line to the function at that point.
In this case the slope of the tangent line to the function at x=2 is -1/4. That means the value of the derivative of the function at x=2 is -1/4. f'(2) = -1/4.
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